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This is a puzzle about a man condemned to be hanged. The man was sentenced on Saturday. “The hanging will take place at noon,” said the judge to the prisoner, “on one of the seven days of next week. But you will not know which day it is until you are informed on the morning of the day of the hanging.”
The judge was known to be a man who always kept his word. The prisoner, accompanied by his lawyer, went back to his cell. As soon as the two men were alone the lawyer broke into a grin. “Don’t you see?” he exclaimed. “The judge’s sentenced cannot possibly be carried out.”
“I don’t understand,” said the prisoner. “Let me explain. They obviously cannot hang you next Saturday. Saturday is the last day of the week. On Friday afternoon, you will still be alive and know with certainty that the hanging will be on Saturday. You would know this before you were told on Saturday morning. That would violate the judge’s decree.”
“True,” said the prisoner. “Therefore, Saturday is ruled out,” continued the lawyer. “This leaves Friday as the last day they can hang you. But they can’t hang you on Friday because by Thursday afternoon, only two days would remain : Friday and Saturday. Since Saturday is not possible, the hanging would have to be on Friday. Your knowledge of this fact would again violate the judge’s decree. So Friday is out. This leaves Thursday as the last possible day. But Thursday is out because if you are alive on Wednesday afternoon, you will know that Thursday will be the day.”
“I get it,” said the prisoner, who was beginning to feel much better. “In exactly the same way I can rule out Wednesday, Tuesday and Monday. That leaves only tomorrow. But they can’t hang me tomorrow because I know it today!”
The prisoner is thus convinced, by what appears to be unimpeachable logic, that he cannot be hanged without violating the judge’s decree. Then, on Thursday morning, the hangman arrives. Clearly, the prisoner did not expect him. What is more surprising, the conditions stated by the judge is now fulfilled.
What went wrong with the reasoning provided by the lawyer?